%0 Journal Article
%T Pinched exponential volume growth implies an infinite dimensional isoperimetric inequality
%A Itai Benjamini
%A Oded Schramm
%J Mathematics
%D 2003
%I arXiv
%X Let $G$ be a graph which satisfies $c^{-1} a^r \le |B(v,r)| \le c a^r$, for some constants $c,a>1$, every vertex $v$ and every radius $r$. We prove that this implies the isoperimetric inequality $|\partial A| \ge C |A| / \log(2+ |A|)$ for some constant $C=C(a,c)$ and every finite set of vertices $A$.
%U http://arxiv.org/abs/math/0303127v1